## Degrees of freedom of TaaTP [Power / Sample Size]

Dear Helmut, dear Olivbood,

» ...

» » Furthermore, while the two parts of the trial will be evaluated as incomplete block designs, it seems to me that the original sequences and periods are preserved (e.g. an observation from period 3 is still coded as period 3), so that the degree of freedom would not be the same as for the conventional 2x2x2 crossover, no?

»

» Correct. Has some strange side-effects (see there).

To repeat the recommendation in this post:

(TaaTP: Two-at-a-Time Principle)

But makes seldom a difference worth thinkin' about:

2 subjects more but due to balanced design, i.e. sample size has to be a multiple of 6.

If we go for an unbalanced design we have also a power of 90% with 52 subjects:

» ...

» » Furthermore, while the two parts of the trial will be evaluated as incomplete block designs, it seems to me that the original sequences and periods are preserved (e.g. an observation from period 3 is still coded as period 3), so that the degree of freedom would not be the same as for the conventional 2x2x2 crossover, no?

»

» Correct. Has some strange side-effects (see there).

To repeat the recommendation in this post:

*The degrees of freedom are different for the 2x2 design and the design of the TaaTP.*

We can mimic the df's, at leastWe can mimic the df's, at least

**approximately**, if we use the robust df's.(TaaTP: Two-at-a-Time Principle)

But makes seldom a difference worth thinkin' about:

`library(PowerTOST)`

sampleN.TOST(CV=0.3, design="2x2x2", targetpower=0.9, print=FALSE)

Design alpha CV theta0 theta1 theta2 Sample size Achieved power Target power

1 2x2x2 0.05 0.3 0.95 0.8 1.25 52 0.9019652 0.9

sampleN.TOST(CV=0.3, design="3x6x3", targetpower=0.9, robust=TRUE, print=FALSE)

Design alpha CV theta0 theta1 theta2 Sample size Achieved power Target power

1 3x6x3 0.05 0.3 0.95 0.8 1.25 54 0.9112411 0.9

2 subjects more but due to balanced design, i.e. sample size has to be a multiple of 6.

If we go for an unbalanced design we have also a power of 90% with 52 subjects:

`power.TOST(CV=0.3, design="3x6x3", robust=TRUE, n=52)`

Unbalanced design. n(i)=9/9/9/9/8/8 assumed.

[1] 0.9005174

—

Regards,

Detlew

Regards,

Detlew

### Complete thread:

- Sample Size Calculation for Drug Effect and Food Effect study Olivbood 2019-05-08 16:16 [Power / Sample Size]
- Tricky question, lengthy answer Helmut 2019-05-08 18:02
- Tricky question, lengthy answer Olivbood 2019-05-08 19:20
- Tricky question, lengthy answer Helmut 2019-05-09 00:47

- Tricky question, lengthy answer Olivbood 2019-05-10 21:11
- Tricky question, lengthy answer Helmut 2019-05-14 14:11
- Degrees of freedom of TaaTP d_labes 2019-05-14 16:01
- Use of incomplete block design? Olivbood 2019-05-23 22:30
- Radio Yerevan answers Helmut 2019-05-24 11:28

- Use of incomplete block design? Olivbood 2019-05-23 22:30

- Degrees of freedom of TaaTP d_labes 2019-05-14 16:01

- Tricky question, lengthy answer Helmut 2019-05-14 14:11

- Tricky question, lengthy answer Olivbood 2019-05-08 19:20

- Tricky question, lengthy answer Helmut 2019-05-08 18:02